The main types of sets in algebra are the finite set, the infinite set, the singleton set, the null set, the subset and the proper set. A finite set is a set that has a predetermined number of elements as its members, while an infinite set does not have a predetermined number of elements, although it typically contains uncountable elements. The set of integers is an infinite set.

A set that contains only one element is known as a singleton set, while a set that contains no elements is referred to as a null or void set. Some common set operations include the union of sets and the intersection of sets. The union of sets typically contains all the elements of the sets that make up the union, but in the union of two sets, the elements in both sets are written only once, even if they appear in both sets. The intersection of sets consists of all the elements that are common in all the intersecting sets. There are several laws that govern set operations, which include the commutative, associative and distributive laws, which are all applicable to set unions and intersections. These laws are the basis for the derivation of the identity laws.